Predicting Divisional Winners

Date: 07/29/99 at 15:53:28
From: Jackie
Subject: Probability
There are seven teams in each of the two divisions of American League
baseball, and six teams in each of the two divisions of the National
League. A sportswriter "predicts" the winner of the four divisions by
choosing a team completely at random in each division.
A. What is the probability that the sportswriter will predict at least
one winner correctly?
B. Suppose that the sportswriter eliminates from each division one
team that clearly has no chance of winning, and predicts the winner
from each division from the remaining teams. Assuming that the
eliminated teams do not end up surprising anyone, what is the
writer's chance of predicting at least two winners?
C. Suppose the writer puts all 26 teams in a hat and draws four teams
at random. Does this increase or decrease the writer's chance of
picking at least one winner?